Modern Electrochemistry

CONTENTS......Page 16
6.1.2. New Forces at the Boundary of an Electrolyte......Page 30
6.1.4. An Electrode Is Like a Giant Central Ion......Page 33
6.1.6. Both Sides of the Interface Become Electrified: The Electrical Double Layer......Page 34
6.1.8. What Knowledge Is Required before an Electrified Interface Can Be Regarded as Understood?......Page 37
6.1.10. Why Bother about Electrified Interfaces?......Page 39
6.2.2. The Importance of Working with Clean Surfaces (and Systems)......Page 41
6.2.3. Why Use Single Crystals?......Page 43
6.2.4. In Situ vs. Ex Situ Techniques......Page 44
6.2.5. Ex Situ Techniques......Page 47
6.2.6. In Situ Techniques......Page 56
6.3.1. What Happens When One Tries to Measure the Potential Difference Across a Single Electrode/Electrolyte Interface?......Page 65
6.3.2. Can One Measure Changes in the Metal–Solution Potential Difference?......Page 70
6.3.3. The Extreme Cases of Ideally Nonpolarizable and Polarizable Interfaces......Page 72
6.3.4. The Development of a Scale of Relative Potential Differences......Page 74
6.3.5. Can One Meaningfully Analyze an Electrode–Electrolyte Potential Difference?......Page 76
6.3.6. The Outer Potential ψ of a Material Phase in a Vacuum......Page 80
6.3.7. The Outer Potential Difference, [sup(M)]Δ[sup(S)]ψ between the Metal and the Solution......Page 81
6.3.8. The Surface Potential, χ, of a Material Phase in a Vacuum......Page 82
6.3.9. The Dipole Potential Difference [sup(M)]Δ[sup(S)]χ across an Electrode–Electrolyte Interface......Page 83
6.3.10. The Sum of the Potential Differences Due to Charges and Dipoles: The Inner Potential Difference, [sup(M)]Δ[sup(S)]Φ......Page 85
6.3.11. The Outer, Surface, and Inner Potential Differences......Page 87
6.3.12. Is the Inner Potential Difference an Absolute Potential Difference?......Page 88
6.3.13. The Electrochemical Potential, the Total Work from Infinity to Bulk......Page 89
6.3.14. The Electron Work Function, Another Interfacial Potential......Page 93
6.3.15. The Absolute Electrode Potential......Page 96
6.4.1. What Would Represent Complete Structural Information on an Electrified Interface?......Page 101
6.4.2. The Concept of Surface Excess......Page 102
6.4.3. Is the Surface Excess Equivalent to the Amount Adsorbed?......Page 104
6.4.4. Does Knowledge of the Surface Excess Contribute to Knowledge of the Distribution of Species in the Interphase Region?......Page 105
6.4.5. Is the Surface Excess Measurable?......Page 106
6.5.1. The Measurement of Interfacial Tension as a Function of the Potential Difference across the Interface......Page 107
6.5.2. Some Basic Facts about Electrocapillary Curves......Page 111
6.5.3. Some Thermodynamic Thoughts on Electrified Interfaces......Page 113
6.5.4. Interfacial Tension Varies with Applied Potential: Determination of the Charge Density on the Electrode......Page 117
6.5.5. Electrode Charge Varies with Applied Potential: Determination of the Electrical Capacitance of the Interface......Page 118
6.5.6. The Potential at which an Electrode Has a Zero Charge......Page 120
6.5.7. Surface Tension Varies with Solution Composition: Determination of the Surface Excess......Page 121
6.5.8. Summary of Electrocapillary Thermodynamics......Page 125
6.5.9. Retrospect and Prospect for the Study of Electrified Interfaces......Page 128
6.6.1 A Look into an Electrified Interface......Page 130
6.6.2. The Parallel-Plate Condenser Model: The Helmholtz–Perrin Theory......Page 132
6.6.4. The Ionic Cloud: The Gouy–Chapman Diffuse-Charge Model of the Double Layer......Page 135
6.6.5. The Gouy–Chapman Model Provides a Potential Dependence of the Capacitance, but at What Cost?......Page 139
6.6.6. Some Ions Stuck to the Electrode, Others Scattered in Thermal Disarray: The Stern Model......Page 141
6.6.7. The Contribution of the Metal to the Double-Layer Structure......Page 146
6.6.8. The Jellium Model of the Metal......Page 149
6.6.9. How Important Is the Surface Potential for the Potential of the Double Layer?......Page 152
6.7.1. An Electrode Is Largely Covered with Adsorbed Water Molecules......Page 154
6.7.2. Metal–Water Interactions......Page 155
6.7.3. One Effect of the Oriented Water Molecules in the Electrode Field: Variation of the Interfacial Dielectric Constant......Page 156
6.7.4. Orientation of Water Molecules on Electrodes: The Three-State Water Model......Page 157
6.7.5. How Does the Population of Water Species Vary with the Potential of the Electrode?......Page 159
6.7.6. The Surface Potential, g[sup(S)sub(dipole)], Due to Water Dipoles......Page 163
6.7.7. The Contribution of Adsorbed Water Dipoles to the Capacity of the Interface......Page 169
6.7.8. Solvent Excess Entropy of the Interface: A Key to Obtaining Structural Information on Interfacial Water Molecules......Page 171
6.7.9. If Not Solvent Molecules, What Factors Are Responsible for Variation in the Differential Capacity of the Electrified Interface with Potential?......Page 174
6.8.1. How Close Can Hydrated Ions Come to a Hydrated Electrode?......Page 178
6.8.2. What Parameters Determine if an Ion Is Able to Contact Adsorb on an Electrode?......Page 179
6.8.3. The Enthalpy and Entropy of Adsorption......Page 185
6.8.4. Effect of the Electrical Field at the Interface on the Shape of the Adsorbed Ion......Page 188
6.8.5. Equation of States in Two Dimensions......Page 190
6.8.6. Isotherms of Adsorption in Electrochemical Systems......Page 192
6.8.7. A Word about Standard States in Adsorption Isotherms......Page 195
6.8.8. The Langmuir Isotherm: A Fundamental Isotherm......Page 196
6.8.10. The Temkin Isotherm: A Heterogeneous Surface Isotherm......Page 197
6.8.12. Applicability of the Isotherms......Page 200
6.8.13. An Ionic Isotherm for Heterogeneous Surfaces......Page 203
6.8.14. Thermodynamic Analysis of the Adsorption Isotherm......Page 214
6.8.15. Contact Adsorption: Its Influence on the Capacity of the Interface......Page 218
6.8.16. Looking Back......Page 222
6.9.1. The Relevance of Organic Adsorption......Page 227
6.9.2. Is Adsorption the Only Process that the Organic Molecules Can Undergo?......Page 228
6.9.3. Identifying Organic Adsorption......Page 229
6.9.4. Forces Involved in Organic Adsorption......Page 230
6.9.5. The Parabolic Coverage-Potential Curve......Page 231
6.9.6. Other Factors Influencing the Adsorption of Organic Molecules on Electrodes......Page 237
6.10.1. The Structure of the Semiconductor–Electrolyte Interface......Page 243
6.10.2. Colloid Chemistry......Page 260
6.11.1. The Phenomenology of Mobile Electrified Interfaces: Electrokinetic Properties......Page 265
6.11.2. The Relative Motion of One of the Phases Constituting an Electrified Interface Produces a Streaming Current......Page 267
6.11.3. A Potential Difference Applied Parallel to an Electrified Interface Produces an Electro-osmotic Motion of One of the Phases Relative to the Other......Page 270
6.11.4. Electrophoresis: Moving Solid Particles in a Stationary Electrolyte......Page 271
Exercises......Page 274
Problems......Page 279
Micro Research Problems......Page 288
Appendix 6.1......Page 290
7.1.1. Some Things One Has to Know About Interfacial Electron Transfer: It’s Both Electrical and Chemical......Page 294
7.1.3. The Three Possible Electrochemical Devices......Page 295
7.1.4. Some Special Characteristics of Electrochemical Reactions......Page 300
7.2. Electron Transfer Under an Interfacial Electric Field......Page 301
7.2.1. A Two-Way Traffic Across the Interface: Equilibrium and the Exchange Current Density......Page 306
7.2.2. The Interface Out of Equilibrium......Page 308
7.2.3. A Quantitative Version of the Dependence of the Electrochemical Reaction Rate on Overpotential: The Butler–Volmer Equation......Page 311
7.2.4. Polarizable and Nonpolarizable Interfaces......Page 314
7.2.5. The Equilibrium State for Charge Transfer at the Metal/Solution Interface Treated Thermodynamically......Page 316
7.2.7. The Equilibrium Condition: Nernst’s Thermodynamic Treatment......Page 317
7.2.8. The Final Nernst Equation and the Question of Signs......Page 321
7.2.9. Why Is Nernst’s Equation of 1904 Still Useful?......Page 323
7.2.10. Looking Back to Look Forward......Page 324
7.3. A More Detailed Look at Some Quantities in the Butler–Volmer Equation......Page 326
7.3.1. Does the Structure of the Interphasial Region Influence the Electrochemical Kinetics There?......Page 327
7.3.2. What About the Theory of the Symmetry Factor, β?......Page 330
7.3.3. The Interfacial Concentrations May Depend on Ionic Transport in the Electrolyte......Page 331
7.4.1. Introduction......Page 333
7.4.2. The Current-Potential Relation at a Semiconductor/Electrolyte Interface (Negligible Surface States)......Page 341
7.4.4. The Use of n- and p-Semiconductors for Thermal Reactions......Page 345
7.4.5. The Limiting Current in Semiconductor Electrodes......Page 347
7.4.6. Photoactivity of Semiconductor Electrodes......Page 348
7.5.1. Preparing the Solution......Page 350
7.5.2. Preparing the Electrode Surface......Page 353
7.5.3. Real Area......Page 354
7.5.4. Microelectrodes......Page 356
7.5.6. Which Electrode System Is Best?......Page 362
7.5.7. The Measurement Cell......Page 363
7.5.8. Keeping the Current Uniform on an Electrode......Page 370
7.5.9. Apparatus Design Arising from the Needs of the Electronic Instrumentation......Page 371
7.5.10. Measuring the Electrochemical Reaction Rate as a Function of Potential (at Constant Concentration and Temperature)......Page 374
7.5.11. The Dependence of Electrochemical Reaction Rates on Temperature......Page 381
7.5.12. Electrochemical Reaction Rates as a Function of the System Pressure......Page 382
7.5.13. Impedance Spectroscopy......Page 386
7.5.14. Rotating Disk Electrode......Page 398
7.5.15. Spectroscopic Approaches to Electrode Kinetics .......Page 404
7.5.16. Ellipsometry......Page 406
7.5.17. Isotopic Effects......Page 413
7.5.18. Atomic-Scale In Situ Microscopy......Page 416
7.5.19. Use of Computers in Electrochemistry......Page 418
7.6.1. The Difference between Single-Step and Multistep Electrode Reactions......Page 425
7.6.3. The Catalytic Pathway......Page 426
7.6.5. Rate-Determining Steps in the Cathodic Hydrogen Evolution Reaction......Page 427
7.6.6. Some Ideas on Queues, or Waiting Lines......Page 428
7.6.7. The Overpotential η Is Related to the Electron Queue at an Interface......Page 430
7.6.8. A Near-Equilibrium Relation between the Current Density and Overpotential for a Multistep Reaction......Page 431
7.6.9. The Concept of a Rate-Determining Step......Page 434
7.6.10. Rate-Determining Steps and Energy Barriers for Multistep Reactions......Page 439
7.6.11. How Many Times Must the Rate-Determining Step Take Place Number for the Overall Reaction to Occur Once? The Stoichiometric Number ν......Page 441
7.6.12. The Order of an Electrodic Reaction......Page 446
7.6.13. Blockage of the Electrode Surface during Charge Transfer: The Surface-Coverage Factor......Page 449
7.7.1. Heat of Adsorption Independent of Coverage......Page 452
7.7.2. Heat of Adsorption Dependent on Coverage......Page 453
7.7.4. Consequences from the Frumkin–Temkin Isotherm......Page 454
7.7.6. Are the Electrode Kinetics Affected in Circumstances under which ΔG[sub(θ) Varies with θ?......Page 456
7.8.2. Single Crystals and Planes of Specific Orientation......Page 460
7.8.3. Another Preliminary: The Voltammogram as the Arbiter of a Clean Surface......Page 462
7.8.4. Examples of the Different Degrees of Reactivity Caused by Exposing Different Planes of Metal Single Crystals to the Solution......Page 464
7.8.5. General Assessment of Single-Crystal Work in Electrochemistry......Page 468
7.8.6. Roots of the Work on Kinetics at Single-Crystal Planes......Page 469
7.9.1. Ionics Looks after the Material Needs of the Interface......Page 470
7.9.2. How the Transport Flux Is Linked to the Charge-Transfer Flux: The Flux-Equality Condition......Page 472
7.9.3. Appropriations from the Theory of Heat Transfer......Page 474
7.9.4. A Qualitative Study of How Diffusion Affects the Response of an Interface to a Constant Current......Page 475
7.9.5. A Quantitative Treatment of How Diffusion to an Electrode Affects the Response with Time of an Interface to a Constant Current......Page 477
7.9.6. The Concept of Transition Time......Page 480
7.9.7. Convection Can Maintain Steady Interfacial Concentrations......Page 484
7.9.8. The Origin of Concentration Overpotential......Page 489
7.9.9. The Diffusion Layer......Page 491
7.9.10.The Limiting Current Density and Its Practical Importance......Page 494
7.9.11.The Steady-State Current–Potential Relation under Conditions of Transport Control......Page 505
7.9.13.The Concentration of Charge Carriers at the Electrode......Page 506
7.9.14.Current as a Function of Overpotential: Interfacial and Diffusion Control......Page 507
7.9.15.The Reciprocal Relation......Page 509
7.9.16. Reversible and Irreversible Reactions......Page 510
7.9.17. Transport-Controlled Deelectronation Reactions......Page 511
7.9.18. What Is the Effect of Electrical Migration on the Limiting Diffusion Current Density?......Page 512
7.9.19. Some Summarizing Remarks on the Transport Aspects of Electrodics......Page 513
7.10.1. Why Bother about Determining a Mechanism?......Page 516
7.10.2. What Does It Mean: “To Determine the Mechanism of an Electrode Reaction”?......Page 517
7.10.3. The Mechanism of Reduction of O[sub(2)] on Iron at Intermediate pH’s......Page 522
7.10.4. Mechanism of the Oxidation of Methanol......Page 528
7.10.5. The Importance of the Steady State in Electrode Kinetics......Page 533
7.11.1. Introduction......Page 534
7.11.2. At What Potential Should the Relative Power of Electrocatalysts Be Compared?......Page 536
7.11.3. How Electrocatalysis Works......Page 539
7.11.4. Volcanoes......Page 543
7.11.5. Is Platinum the Best Catalyst?......Page 545
7.11.6. Bioelectrocatalysis......Page 546
7.12.1. The Two Aspects of Electrogrowth......Page 552
7.12.2. The Reaction Pathway for Electrodeposition......Page 553
7.12.3. Stepwise Dehydration of an Ion; the Surface Diffusion of Adions......Page 555
7.12.4. The Half-Crystal Position......Page 560
7.12.5. Deposition on an Ideal Surface: The Resulting Nucleation......Page 561
7.12.6. Values of the Minimum Nucleus Size Necessary for Continued Growth......Page 564
7.12.7. Rate of an Electrochemical Reaction Dependent on 2D Nucleation......Page 565
7.12.8. Surface Diffusion to Growth Sites......Page 566
7.12.9. Residence Time......Page 569
7.12.10. The Random Thermal Displacement......Page 571
7.12.11. Underpotential Deposition......Page 572
7.12.12. Some Devices for Building Lattices from Adions: Screw Dislocations and Spiral Growths......Page 575
7.12.13. Microsteps and Macrosteps......Page 583
7.12.14. How Steps from a Pair of Screw Dislocations Interact......Page 586
7.12.15. Crystal Facets Form......Page 587
7.12.17. Deposition on Single-Crystal and Polycrystalline Substrates......Page 593
7.12.18. How the Diffusion of Ions in Solution May Affect Electrogrowth......Page 594
7.12.19. About the Variety of Shapes Formed in Electrodeposition......Page 595
7.12.20. Dendrites......Page 597
7.12.21. Organic Additives and Electrodeposits......Page 598
7.12.22. Material Failures Due to H Co-deposition......Page 599
7.12.24. Breakdown Potentials for Certain Organic Solvents......Page 600
7.12.25. Molten Salt Systems Avoid Hydrogen Codeposition......Page 603
7.12.28. Electrochemical Nanotechnology......Page 604
7.13.1. The Potential Difference across an Electrochemical System......Page 607
7.13.2. The Equilibrium Potential Difference across an Electrochemical Cell......Page 609
7.13.3. The Problem with Tables of Standard Electrode Potentials......Page 610
7.13.4. Are Equilibrium Cell Potential Differences Useful?......Page 615
7.13.5. Electrochemical Cells: A Qualitative Discussion of the Variation of Cell Potential with Current......Page 620
7.13.6. Electrochemical Cells in Action: Some Quantitative Relations between Cell Current and Cell Potential......Page 623
7.14. The Electrochemical Activation of Chemical Reactions......Page 630
7.15.2. Electroless Metal Deposition......Page 633
7.15.3. Heterogeneous “Chemical” Reactions in Solutions......Page 635
7.15.4. Electrogenerative Synthesis......Page 636
7.15.5. Magnetic Induction......Page 637
7.16. The Electrochemical Heart......Page 639
Further Reading......Page 641
8.1.1. The Evolution of Short Time Measurements......Page 660
8.1.2. Another Reason for Making Transient Measurements......Page 662
8.1.4. General Comment on Factors in Achieving Successful Transient Measurements......Page 666
8.2.1. How They Work......Page 668
8.2.2. Chronopotentiometry......Page 670
8.3.1. The Mathematics......Page 671
8.4.1. The Method......Page 673
8.5.1. Reversal Techniques......Page 675
8.5.2. Summary of Transient Methods......Page 676
8.5.3. “Totally Irreversible,” etc.: Some Aspects of Terminology......Page 677
8.5.4. The Importance of Transient Techniques......Page 679
8.6.1. Introduction......Page 681
8.6.2. Beginning of Cyclic Voltammetry......Page 683
8.6.3. The Range of the Cyclic Voltammetric Technique......Page 684
8.6.4. Cyclic Voltammetry: Its Limitations......Page 685
8.6.5. The Acceptable Sweep Rate Range......Page 686
8.6.6. The Shape of the Peaks in Potential-Sweep Curves......Page 687
8.6.7. Quantitative Calculation of Kinetic Parameters from Potential–Sweep Curves......Page 690
8.6.8. Some Examples......Page 691
8.6.10. Two Difficulties in Cyclic Voltammetric Measurements......Page 693
8.7.1. Potentiodynamic Relations that Account for the Role of Adsorbed Intermediates......Page 697
9.1. Setting the Scene......Page 714
9.1.1. A Preliminary Discussion: Absolute or Vacuum-Scale Potentials......Page 716
9.2.1. The “Fermi Energy” of Electrons in Solution......Page 717
9.2.2. The Electrochemical Potential of Electrons in Solution and Their Quantal Energy States......Page 720
9.2.3. The Importance of Distribution Laws......Page 721
9.2.4. Distribution of Energy States in Solution: Introduction......Page 722
9.2.5. The Distribution Function for Electrons in Metals......Page 728
9.2.6. The Density of States in Metals......Page 730
9.3.1. Introduction......Page 732
9.3.2. The Basic Potential Energy Diagram......Page 734
9.3.3. Electrode Potential and the Potential Energy Curves......Page 738
9.3.4. How Bonding of Surface Radicals to the Electrode Produces Electrocatalysis......Page 743
9.3.5. Harmonic and Anharmonic Curves......Page 746
9.3.6. How Many Dimensions?......Page 747
9.4.1. The Idea......Page 748
9.4.2. Equations of Tunneling......Page 749
9.4.3. The WKB Approximation......Page 751
9.4.5. Other Approaches to Quantum Transitions and Some Problems......Page 753
9.4.6. Tunneling through Adsorbed Layers at Electrodes and in Biological Systems......Page 754
9.5.2. Outer Shell and Inner Shell Reactions......Page 755
9.5.4. Adiabatic and Nonadiabatic Electrode Reactions......Page 756
9.6.1. Electron Transfer......Page 758
9.6.3. What Happens if the Movements of the Solvent–Ion Bonds Are Taken as a Simple Harmonic? An Aberrant Expression for Free Energy Activation in.........Page 763
9.6.4. The Primacy of Tafel’s Law in Experimental Electrode Kinetics......Page 766
9.7.1. Origin of the Energy of Activation......Page 770
9.7.2. Weiss–Marcus: Electrostatic......Page 771
9.7.3. George and Griffith’s Thermal Model......Page 773
9.7.4. Fluctuations of the Ground State Model......Page 774
9.7.5. The Librator Fluctuation Model......Page 775
9.7.6. The Vibron Model......Page 776
9.8.1. Introduction......Page 777
9.9.1. Equations......Page 780
9.10.1. Discussion......Page 781
A.1. Introduction: Gurney–Butler......Page 785
A.3. The Dark Side of β......Page 787
B......Page 794
C......Page 795
D......Page 797
E......Page 798
F......Page 802
G......Page 803
H......Page 804
I......Page 805
K......Page 806
M......Page 807
N......Page 808
O......Page 809
P......Page 810
R......Page 812
S......Page 813
T......Page 815
W......Page 816
Z......Page 817